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- Title
Democracy of quasi-greedy bases in $\boldsymbol p$ -Banach spaces with applications to the efficiency of the Thresholding Greedy Algorithm in the Hardy spaces $\boldsymbol {H_{p}({\mathbb {D}}^{d})}$.
- Authors
Albiac, Fernando; Ansorena, José L.; Bello, Glenier
- Abstract
We use new methods, specific for non-locally convex quasi-Banach spaces, to investigate when the quasi-greedy bases of a $p$ -Banach space for $0 are democratic. The novel techniques we obtain permit to show in particular that all quasi-greedy bases of the Hardy space $H_p({\mathbb {D}})$ for $0 are democratic while, in contrast, no quasi-greedy basis of $H_p({\mathbb {D}}^d)$ for $d\ge 2$ is, solving thus a problem that was raised in [7]. Applications of our results to other spaces of interest both in functional analysis and approximation theory are also provided.
- Subjects
THRESHOLDING algorithms; GREEDY algorithms; HARDY spaces; APPROXIMATION theory; FUNCTIONAL analysis; DEMOCRACY
- Publication
Proceedings of the Royal Society of Edinburgh: Section A: Mathematics, 2024, Vol 154, Issue 3, p906
- ISSN
0308-2105
- Publication type
Article
- DOI
10.1017/prm.2023.42